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Higher-order symmetric duality with higher-order generalized invexity. (English) Zbl 1342.90219

The authors establish new weak, strong and converse duality results for the higher-order symmetric dual problems under appropriate invexity hypotheses.

MSC:

90C46 Optimality conditions and duality in mathematical programming
90C30 Nonlinear programming

Keywords:

duality; invexity
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References:

[1] Ahamd, I., Husain, Z.: On multiobjective second order symmetric duality with cone constraints. Eur. J. Oper. Res. 204, 402-409 (2010) · Zbl 1181.90236 · doi:10.1016/j.ejor.2009.08.019
[2] Bazaraa, M.S., Goode, J.J.: On symmetric duality in nonlinear programming. Oper. Res. 21, 1-9 (1973) · Zbl 0259.90034 · doi:10.1287/opre.21.1.1
[3] Bector, C.R., Chandra, S.: Generalized bonvexity and higher duality for fractional programming. Opsearch 24, 143-154 (1987) · Zbl 0638.90095
[4] Chandra, S., Kumar, V.: A note on pseudo-invexity and symmetric duality. Eur. J. Oper. Res. 105, 626-629 (1998) · Zbl 0955.90125 · doi:10.1016/S0377-2217(97)00087-8
[5] Chen, X.: Higher order symmetric duality in non-differentiable multiobjective programming problems. J. Math. Anal. Appl. 290, 423-435 (2004) · Zbl 1044.90055 · doi:10.1016/j.jmaa.2003.10.004
[6] Dantzig, G.B., Eisenberg, E., Cottle, R.W.: Symmetric dual nonlinear programs. Pac. J. Math. 15, 809-812 (1965) · Zbl 0136.14001 · doi:10.2140/pjm.1965.15.809
[7] Dorn, W.S.: A symmetric dual theorem for quadratic programs. J. Opes. Res. Soc. Jpn. 2, 93-97 (1960)
[8] Gulati, T.R., Ahmad, I., Husain, I.: Second-order symmetric duality with generalized convexity. Opsearch 38, 210-222 (2001) · Zbl 1278.90431
[9] Gulati, T.R., Gupta, S.K.: Higher-order symmetric duality with cone constraints. Appl. Math. Lett. 22, 776-781 (2009) · Zbl 1189.90154 · doi:10.1016/j.aml.2008.08.017
[10] Kassem, M.: Multiobjective nonlinear second order symmetric duality with \[(K, F)(K,F)\]-pseudoconvexity. Appl. Math. Comput. 219, 2142-2148 (2012) · Zbl 1291.90223 · doi:10.1016/j.amc.2012.08.060
[11] Mangasarian, O.L.: Second and higher order duality in nonlinear programming. J. Math. Anal. Appl. 51, 607-620 (1975) · Zbl 0313.90052 · doi:10.1016/0022-247X(75)90111-0
[12] Mishra, S.K.: Second-order symmetric duality in mathematical programming with F-convexity. Eur. J. Oper. Res. 127, 507-518 (2000) · Zbl 0982.90063 · doi:10.1016/S0377-2217(99)00334-3
[13] Mishra, S.K., Rueda, N.G.: Higher-order generalized invexity and duality in mathematical programming. J. Math. Anal. Appl. 247, 173-182 (2000) · Zbl 1056.90136 · doi:10.1006/jmaa.2000.6842
[14] Mond, B.: Second order duality for nonlinear programs. Opsearch 11, 90-99 (1974)
[15] Mond, B.; Weir, T.; Kumar, S. (ed.), Symmetric duality for nonlinear multiobjective programming, 137-153 (1991), London · Zbl 0787.90083
[16] Mond, B.; Zhang, J.; Crouzeix, JP (ed.); etal., Higher-order invexity and duality in mathematical programming, 357-372 (1998), Dordrecht · Zbl 0932.90039 · doi:10.1007/978-1-4613-3341-8_17
[17] Padhan, SK; Nahak, C., Second order symmetric duality with generalized invexity, 205-214 (2011), New York · Zbl 1247.90286 · doi:10.1007/978-1-4419-9640-4_12
[18] Padhan, S.K., Nahak, C.: Higher-order symmetric duality in multiobjective programming problems under higher-order invexity. Appl. Math. Comput. 5, 1705-1712 (2011) · Zbl 1254.90215 · doi:10.1016/j.amc.2011.06.049
[19] Suneja, S.K., Lalitha, C.S., Khurana, S.: Second-order symmetric duality in multiobjective programming. Eur. J. Oper. Res. 144, 492-500 (2003) · Zbl 1028.90050 · doi:10.1016/S0377-2217(02)00154-6
[20] Unger, P.S., Hunter Jr, A.P.: The dual of the dual as linear approximation of the primal. Int. J. Syst. Sci. 12, 1119-1130 (1974) · Zbl 0376.90085 · doi:10.1080/00207727408920166
[21] Yang, X.M., Yang, X.Q., Teo, K.L.: Higher-order symmetric duality in multiobjective mathematical programming with invexity. J. Ind. Manag. Optim. 4, 335-391 (2008) · Zbl 1161.90485
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